Find the Properties x^2=12y

Problem

x^2=12*y

Solution

1. Identify the form of the parabola. The equation x^2=12*y is in the standard form x^2=4*p*y which represents a parabola that opens upward with its vertex at the origin.

2. Determine the value of p By comparing x^2=12*y to x^2=4*p*y we set 4*p=12

4*p=12

p=3

3. Find the vertex. Since the equation is in the form x^2=4*p*y the vertex is at the origin.

Vertex=(0,0)

4. Find the focus. For a parabola opening upward, the focus is located at (0,p)

Focus=(0,3)

5. Find the directrix. The directrix is a horizontal line given by the equation y=−p

Directrix:y=−3

6. Identify the axis of symmetry. Since the x term is squared and the vertex is at the origin, the axis of symmetry is the yaxis.

Axis of Symmetry:x=0

7. Calculate the focal diameter (length of the latus rectum). The length is given by |4*p|

Focal Diameter=|12|=12

Final Answer

Vertex: *(0,0), Focus: *(0,3), Directrix: *y=−3, Axis of Symmetry: *x=0

Want more problems? Check here!